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2016 Nondense Orbits for Anosov Diffeomorphisms of the $2$-Torus
Jimmy Tseng
Real Anal. Exchange 41(2): 307-314 (2016).


Let $\lambda$ denote the probability Lebesgue measure on $\mathbb{T}^2$. For any $C^2$-Anosov diffeomorphism of the $2$-torus preserving $\lambda$ with measure-theoretic entropy equal to topological entropy, we show that the set of points with nondense orbits is hyperplane absolute winning (HAW). This generalizes the result of Tseng (2009) for $C^2$-expanding maps of the circle.


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Jimmy Tseng. "Nondense Orbits for Anosov Diffeomorphisms of the $2$-Torus." Real Anal. Exchange 41 (2) 307 - 314, 2016.


Published: 2016
First available in Project Euclid: 30 March 2017

zbMATH: 1384.37039
MathSciNet: MR3597322

Primary: 37D05
Secondary: 28A78

Keywords: Anosov diffeomorphisms , nondense orbits , winning sets

Rights: Copyright © 2016 Michigan State University Press

Vol.41 • No. 2 • 2016
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